In 1981, Leviant devised a figure named Enigma eliciting spontaneous perception of rotary motion in absence of real motion. The figure consists of a ray pattern made by narrowly spaced black and white radial lines onto which three chromatic rings are superimposed. A spurious rotation is perceived on the rings. There have been many attempts to explain this intriguing phenomenon, but there is not a commonly accepted explanation that can integrate all the (sometimes contradictory) experimental data. The aim of the present study was to understand if Enigma elicits the same illusory motion also when the rings are not on the same plane of the background. To test this hypothesis we separated at various distances in depth the background of the Enigma illusion and the rings. The size of the rings, in terms of visual angle, was always kept constant. The independent variable was, therefore, the binocular disparity, that changed as a function of the distance of the rings from the background. The observers' task was to rate the strength of the illusory rotary motion perceived on the rings by using a five points scale. The results showed that the effect becomes weaker as the distance between the rings and the background increases. Thus it seems that when binocular disparity increases, the radial lines cannot influence any more the appearance of the rings. It is possible then that the background and the rings are processed as two independent objects. Conclusions will be discussed within the relevant literature.